Average Error: 0.0 → 0.0
Time: 16.3s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[(a \cdot \left(d + b\right) + \left(c \cdot a\right))_*\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original0.0
Target0.0
Herbie0.0
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot \left(\left(b + c\right) + d\right)\]

  2. Taylor expanded around inf 0.0

    \[\leadsto \color{blue}{a \cdot d + \left(a \cdot b + a \cdot c\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{(a \cdot \left(d + b\right) + \left(c \cdot a\right))_*}\]

  4. Final simplification0.0

    \[\leadsto (a \cdot \left(d + b\right) + \left(c \cdot a\right))_*\]

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))

Details

Time bar (total: 15.7s)Debug log

sample28.0ms

Algorithm
intervals

simplify43.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

43.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(* a (+ (+ b c) d))

rewrite4.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

4.0ms
(* a (+ (+ b c) d))

series20.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

20.0ms
(* a (+ (+ b c) d))

simplify255.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

125.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
49.0ms
(+ (* a d) (+ (* a b) (* a c)))
42.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma a (+ d b) (* c a))

rewrite1.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma a (+ d b) (* c a))

series30.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

30.0ms
(fma a (+ d b) (* c a))

simplify129.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

65.0ms
(+ (* a d) (+ (* a b) (* a c)))
64.0ms
(+ (* a d) (+ (* a b) (* a c)))
1.0ms
0

prune102.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* a (+ (+ b c) d)))
0.7b
(cbrt (* a (+ (+ b c) d)))
0.7b
(cbrt (* a (+ (+ b c) d)))
0.5b
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Counts
4 → 73
Calls

4 calls. Slowest were:

11.0ms
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))
2.0ms
(cbrt (* a (+ (+ b c) d)))
2.0ms
(cbrt (* a (+ (+ b c) d)))

series527.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

176.0ms
(* (cbrt (* a (+ (+ b c) d))) (cbrt (* a (+ (+ b c) d))))
137.0ms
(cbrt (* a (+ (+ b c) d)))
107.0ms
(cbrt (* a (+ (+ b c) d)))
107.0ms
(cbrt (* a (+ (+ b c) d)))

simplify7.6s

Counts
49 → 85
Calls

49 calls. Slowest were:

717.0ms
(* (cbrt (* a (- (* (+ b c) (+ b c)) (* d d)))) (cbrt (* a (+ (+ b c) d))))
584.0ms
(* (cbrt (* a (- (* (+ b c) (+ b c)) (* d d)))) (cbrt (* a (+ (pow (+ b c) 3) (pow d 3)))))
547.0ms
(* (cbrt (* a (+ (pow (+ b c) 3) (pow d 3)))) (cbrt (* a (- (* (+ b c) (+ b c)) (* d d)))))

prune983.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (* a (+ (+ b c) d)))
0.7b
(cbrt (* a (+ (+ b c) d)))
0.6b
(cbrt (+ (+ b c) d))
0.5b
(cbrt a)

rewrite12.0ms

Algorithm
rewrite-expression-head
Counts
4 → 51
Calls

4 calls. Slowest were:

4.0ms
(cbrt (* a (+ (+ b c) d)))
4.0ms
(cbrt (* a (+ (+ b c) d)))
3.0ms
(cbrt (+ (+ b c) d))

series692.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

326.0ms
(cbrt a)
170.0ms
(cbrt (+ (+ b c) d))
103.0ms
(cbrt (* a (+ (+ b c) d)))
93.0ms
(cbrt (* a (+ (+ b c) d)))

simplify2.6s

Counts
23 → 63
Calls

23 calls. Slowest were:

429.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))
393.0ms
(cbrt (+ (pow (+ b c) 3) (pow d 3)))
325.0ms
(exp (* -1/3 (+ (log (/ 1 b)) (log (/ 1 a)))))

prune798.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes435.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch2.0ms

end0.0ms

sample1.1s

Algorithm
intervals